Delinquent property taxes may be "purchased" at a tax sale by a private entity, but not by the government. If this happens to your personal residence, you have two years after the tax sale to "redeem" the taxes, that is, pay the tax purchaser the amount of the taxes plus interest, fees, etc. During this time, neither the tax purchaser, nor the government can sell the property based on the tax delinquency. However, the bank can press forward with its foreclosure during this time and obtain an order to sell it at a sheriff's sale before the tax redemption period runs out.
You are referring to a Tax Sale. The taxes can be "sold" and you have the right to redeem, ultimately a final tax sale defeats the mortgage so the lender will ultimately pay the taxes or someone who buys the taxes that are not redeemed will wind up with the property free and clear of the mortgage.
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While your home is in foreclosure you are still the legal owner of the property. Technically it is your responsibility to pay the taxes. Sometimes if the Bank does not want to obtain possession of your property they will not pay the taxes. If after, I believe, 3 years the taxes are not redeemed a 3rd party can buy a tax deed.
Read Mr. Stimson's accurate comment above. In addition, if you are talking about a residential mortgage, the "mortgage company" that is suing you is almost certainly just a bill collector ("servicer"). The bill collectors have contracts with the owners of the mortgages to pay the taxes. The bill collector usually does this just before the tax sale. Sometimes, however, the bill collector waits until after the tax sale. There is usually a redemption period of about 2-1/2 years after the sale, so the bill collector can pay any time, either before the tax sale or during the 2-1/2 years after the sale, without losing the property. That is nerve-racking ordeal for you.
The good news is that, if the bill collector is not just pretending but actually allows the taxes to be sold, it probably means that the bill collector believes it has a weak case for foreclosure and wants to wait and see what happens in the foreclosure case. Do not pay those taxes for the bill collector except under the specific advice of an attorney. You should hire an attorney to investigate whether or not the bill collector has standing to foreclose. Often they do not.
Above all, please do not try to represent yourself.